diff --git a/docs/src/api.md b/docs/src/api.md
index 10a244e5..3de93747 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -172,6 +172,12 @@ mean_vector
 We provide standard mean functions like [`ZeroMean`](@ref) and [`ConstMean`](@ref)
 as well as [`CustomMean`](@ref) to simply wrap a function.
 
+```@docs
+ZeroMean
+ConstMean
+CustomMean
+```
+
 ## Testing Utilities
 
 AbstractGPs provides several consistency tests in the `AbstractGPs.TestUtils` module.
diff --git a/src/mean_function.jl b/src/mean_function.jl
index efb3a954..56ca290d 100644
--- a/src/mean_function.jl
+++ b/src/mean_function.jl
@@ -1,4 +1,6 @@
 """
+    abstract type MeanFunction end
+
 `MeanFunction` introduces an API for treating the prior mean function appropriately.
 On the abstract level, all `MeanFunction` are functions.
 However we generally want to evaluate them on a collection of inputs.
@@ -42,6 +44,20 @@ mean_vector(m::ConstMean, x::AbstractVector) = Fill(m.c, length(x))
 
 A wrapper around whatever unary function you fancy. Must be able to be mapped over an
 `AbstractVector` of inputs.
+
+# Warning
+`CustomMean` is generally sufficient for testing purposes, but care should be taken if
+attempting to differentiate through `mean_vector` with a `CustomMean` when using
+`Zygote.jl`. In particular, `mean_vector(m::CustomMean, x)` is implemented as `map(m.f, x)`,
+which when `x` is a `ColVecs` or `RowVecs` will not differentiate correctly.
+
+In such cases, you should implement `mean_vector` directly for your custom mean.
+For example, if `f(x) = sum(x)`, you might implement `mean_vector` as
+```julia
+mean_vector(::CustomMean{typeof(f)}, x::ColVecs) = vec(sum(x.X; dims=1))
+mean_vector(::CustomMean{typeof(f)}, x::RowVecs) = vec(sum(x.X; dims=2))
+```
+which avoids ever applying `map` to a `ColVecs` or `RowVecs`.
 """
 struct CustomMean{Tf} <: MeanFunction
     f::Tf